Turbomachinery applications generally employ one or more components containing rotating and/or non-rotating airfoils, for example, a compressor or a turbine. When testing the airfoils of such turbomachinery, engineers typically measure a loss of total pressure to gauge the airfoil's performance. Three well-known factors that engender total pressure loss in rows of turbomachinery airfoils are the behavior of the boundary layer along the airfoil surface, the behavior of the boundary layers along the inner and outer diameter end walls to which the airfoil is attached, and the interaction of the airfoil and endwall boundary layers with each other. Current industry practice recognizes the significance and impact of loss control but does not yet fully understand the underlying physics governing the generation of these losses.
A fundamental mechanism of the airfoil is to turn the fluid medium in which it is present. By doing so, the airfoil will develop a distribution of fluid pressure, or a pressure loading, over its surfaces. This distribution is highly dependent on the motion of the fluid near the airfoil surface as determined by the local airfoil geometry. Thus, it is possible to influence the pressure loading of the airfoil by means of airfoil design. Designs that favor placing the bulk of the pressure loading closer to the leading edge of the airfoil are commonly referred to as front-loaded airfoils. Similarly, designs that favor placing the bulk of the pressure loading closer to the trailing edge of the airfoil are commonly referred to as aft-loaded airfoils. The distribution of loading on an airfoil surface is commonly referred to as the loading convention of the airfoil, and members of the turbomachinery industry tend to favor one loading convention over another based on their own experiences and design philosophy.
For instance, most turbomachinery applications employ turbines and/or compressors equipped with airfoils possessing a loading convention distributed uniformly across the span of the airfoil, from root to tip, a practice which is standard within the industry. The airfoils may be positioned relative to one another in order to meet design requirements by varying the working medium fluid area of the passageway, that is, the minimum (or throat) area between two airfoils as measured by the integration along the airfoil span of a minimum distance line from the suction-side of one airfoil to the pressure side of an adjacent airfoil. However, repositioning the airfoils alone will ultimately not improve performance and reduce pressure losses due to the continued use of airfoils embodying standard loading conventions, that is, aft-loaded or front-loaded.
The spanwise distribution of the total pressure loss can be categorized into two distinct regions, each controlled by a separate mechanism. First, the total pressure loss near the middle portion of the airfoil away from the end walls, referred to as the airfoil profile loss, is highly dependent on the behavior of the airfoil surface boundary layer. It has been shown that front-loaded airfoils tend to generate less profile loss than does an aft-loaded airfoil. Likewise, the total pressure loss near the root and tip section of the airfoil close to the end walls, referred to as the secondary loss, is highly dependent on both the end wall boundary layer as well as the interaction of the end wall boundary layer with the airfoil surface boundary layer. It has been shown that aft-loaded airfoils tend to generate less secondary loss than do front-loaded airfoils.
In addition, the amount of loading generated by an airfoil is of interest. Generally, the load value of an airfoil may be expressed as a non-dimensional loading parameter known as the Zweifel load coefficient as known to one of ordinary skill in the art. The Zweifel load coefficient is a ratio of the actual airfoil load to the ideal airfoil load.
The Zweifel load coefficient is calculated according to the following equation:
      Zweifel    ⁢                  ⁢    Load    ⁢                  ⁢    Coefficient    =      2    ⁢          (              s                  B          x                    )        ⁢          cos      2        ⁢                  α        2            ⁡              (                              tan            ⁢                                                  ⁢                          α              2                                +                                                    C                                  X                  ⁢                                                                          ⁢                  1                                                            C                                  X                  ⁢                                                                          ⁢                  2                                                      ⁢            tan            ⁢                                                  ⁢                          α              1                                      )            
where                s is the airfoil pitchwise spacing;        BX is the airfoil axial chord length;        α1 is the airfoil inlet flow angle relative to an axial plane;        α2 is the airfoil exit flow angle relative to an axial plane;        CX1 is the airfoil inlet axial flow velocity; and        CX2 is the airfoil exit axial flow velocity.        
For a given loading per row of airfoils, the loading per airfoil can be controlled by adjusting either or both the airfoil count or the airfoil size. For example, a reduction in either of these two parameters can reduce both weight and cost of the airfoil while in turn increasing the airfoil loading. However, increased airfoil loading may push the airfoil into an unfavorable operational regime with respect to increased airfoil secondary flow losses. For example, high-lift airfoils generally possess a Zweifel load coefficient of greater than 1.2. However, the use of high-lift airfoils for turbomachinery applications is typically avoided due to certain performance obstacles. It has been observed that turbomachinery utilizing high-lift airfoils may exhibit airfoil flow separation or undesirable boundary layer thickening as well as greater secondary losses.
One conventional airfoil design of the prior art achieved a Zweifel load coefficient of up to 1.16 by employing an airfoil having a mixed-loading convention. However, in order to achieve a Zweifel load coefficient greater than 1.16, the size of each airfoil had to be adjusted and/or the number of airfoils had to be changed.
Consequently, there exists a need for a high-lift airfoil design that reduces the total pressure loss by improving both the characteristics of the airfoil and end wall boundary layers, and by minimizing the interaction between the two boundary layers as compared to past mixed-loading airfoils designs.